This chapter provides an overview of recent developments in the design and analysis of cross-over trials. We first consider the analysis of the trial that compares two treatments, A and B, over two periods and where the subjects are randomized to the treatment sequences AB and BA. We make the distinction between fixed and random effects models and show how these models can easily be fitted using modern software. Issues with fitting and testing for a difference in carry-over effects are described and the use of baseline measurements is discussed. Simple methods for testing for a treatment difference when the data are binary are also described. Various designs with two or more treatments but with three or four periods are then described and compared. These include the balanced and partially balanced designs for three or more treatments and designs for factorial treatment combinations. Also described are nearly balanced and nearly strongly balanced designs. Random subject-effects models for the designs with two or more treatments are described and methods for analysing non-normal data are also given. The chapter concludes with a description of the use of cross-over designs in the testing of bioequivalence.

/pdf/design-and-analysis-of-cross-over-trials-4ootbxi8hy.pdf

Design and Analysis of Cross-Over Trials

The Bayesian approach involves synthesising data and judgement in order to reach conclusions about unknown quantities and make predictions. Bayesian methods have become increasingly popular in recent years, notably in medical research, and although there are a number of books on Bayesian analysis, few cover clinical trials and biostatistical applications in any detail. Bayesian Approaches to Clinical Trials and Health-Care Evaluation provides a valuable overview of this rapidly evolving field, including basic Bayesian ideas, prior distributions, clinical trials, observational studies, evidence synthesis and cost-effectiveness analysis. Covers a broad array of essential topics, building from the basics to more advanced techniques.

Bayesian Approaches to Clinical Trials and Health-Care Evaluation: Spiegelhalter/Clinical Trials and Health-Care Evaluation

Preface. List of examples. 1. Introduction. 1.1 What are Bayesian methods? 1.2 What do we mean by 'health--care evaluation'? 1.3 A Bayesian approach to evaluation. 1.4 The aim of this book and the intended audience. 1.5 Structure of the book. 2. Basic Concepts from Traditional Statistical Analysis. 2.1 Probability. 2.1.1 What is probability? 2.1.2 Odds and log--odds. 2.1.3 Bayes theorem for simple events. 2.2 Random variables, parameters and likelihood. 2.2.1 Random variables and their distributions. 2.2.2 Expectation, variance, covariance and correlation. 2.2.3 Parametric distributions and conditional independence. 2.2.4 Likelihoods. 2.3 The normal distribution. 2.4 Normal likelihoods. 2.4.1 Normal approximations for binary data. 2.4.2 Normal likelihoods for survival data. 2.4.3 Normal likelihoods for count responses. 2.4.4 Normal likelihoods for continuous responses. 2.5 Classical inference. 2.6 A catalogue of useful distributionsaeo. 2.6.1 Binomial and Bernoulli. 2.6.2 Poisson. 2.6.3 Beta. 2.6.4 Uniform. 2.6.5 Gamma. 2.6.6 Root--inverse--gamma. 2.6.7 Half--normal. 2.6.8 Log--normal. 2.6.9 Student's t. 2.6.10 Bivariate normal. 2.7 Key points. Exercises. 3. An Overview of the Bayesian Approach. 3.1 Subjectivity and context. 3.2 Bayes theorem for two hypotheses. 3.3 Comparing simple hypotheses: likelihood ratios and Bayes factors. 3.4 Exchangeability and parametric modellingaeo. 3.5 Bayes theorem for general quantities. 3.6 Bayesian analysis with binary data. 3.6.1 Binary data with a discrete prior distribution. 3.6.2 Conjugate analysis for binary data. 3.7 Bayesian analysis with normal distributions. 3.8 Point estimation, interval estimation and interval hypotheses. 3.9 The prior distribution. 3.10 How to use Bayes theorem to interpret trial results. 3.11 The 'credibility' of significant trial resultsaeo. 3.12 Sequential use of Bayes theoremaeo. 3.13 Predictions. 3.13.1 Predictions in the Bayesian framework. 3.13.2 Predictions for binary dataaeo. 3.13.3 Predictions for normal data. 3.14 Decision--making. 3.15 Design. 3.16 Use of historical data. 3.17 Multiplicity, exchangeability and hierarchical models. 3.18 Dealing with nuisance parametersaeo. 3.18.1 Alternative methods for eliminating nuisance parametersaeo. 3.18.2 Profile likelihood in a hierarchical modelaeo. 3.19 Computational issues. 3.19.1 Monte Carlo methods. 3.19.2 Markov chain Monte Carlo methods. 3.19.3 WinBUGS. 3.20 Schools of Bayesians. 3.21 A Bayesian checklist. 3.22 Further reading. 3.23 Key points. Exercises. 4. Comparison of Alternative Approaches to Inference. 4.1 A structure for alternative approaches. 4.2 Conventional statistical methods used in health--care evaluation. 4.3 The likelihood principle, sequential analysis and types of error. 4.3.1 The likelihood principle. 4.3.2 Sequential analysis. 4.3.3 Type I and Type II error. 4.4 P--values and Bayes factorsaeo. 4.4.1 Criticism of P--values. 4.4.2 Bayes factors as an alternative to P--values: simple hypotheses. 4.4.3 Bayes factors as an alternative to P--values: composite hypotheses. 4.4.4 Bayes factors in preference studies. 4.4.5 Lindley's paradox. 4.5 Key points. Exercises. 5. Prior Distributions. 5.1 Introduction. 5.2 Elicitation of opinion: a brief review. 5.2.1 Background to elicitation. 5.2.2 Elicitation techniques. 5.2.3 Elicitation from multiple experts. 5.3 Critique of prior elicitation. 5.4 Summary of external evidenceaeo. 5.5 Default priors. 5.5.1 'Non--informative' or 'reference' priors: 5.5.2 'Sceptical' priors. 5.5.3 'Enthusiastic' priors. 5.5.4 Priors with a point mass at the null hypothesis ('lump--and--smear' priors)aeo. 5.6 Sensitivity analysis and 'robust' priors. 5.7 Hierarchical priors. 5.7.1 The judgement of exchangeability. 5.7.2 The form for the random--effects distribution. 5.7.3 The prior for the standard deviation of the random effectsaeo. 5.8 Empirical criticism of priors. 5.9 Key points. Exercises. 6. Randomised Controlled Trials. 6.1 Introduction. 6.2 Use of a loss function: is a clinical trial for inference or decision? 6.3 Specification of null hypotheses. 6.4 Ethics and randomisation: a brief review. 6.4.1 Is randomisation necessary? 6.4.2 When is it ethical to randomise? 6.5 Sample size of non--sequential trials. 6.5.1 Alternative approaches to sample--size assessment. 6.5.2 'Classical power': hybrid classical--Bayesian methods assuming normality. 6.5.3 'Bayesian power'. 6.5.4 Adjusting formulae for different hypotheses. 6.5.5 Predictive distribution of power and necessary sample size. 6.6 Monitoring of sequential trials. 6.6.1 Introduction. 6.6.2 Monitoring using the posterior distribution. 6.6.3 Monitoring using predictions: 'interim power'. 6.6.4 Monitoring using a formal loss function. 6.6.5 Frequentist properties of sequential Bayesian methods. 6.6.6 Bayesian methods and data monitoring committees. 6.7 The role of 'scepticism' in confirmatory studies. 6.8 Multiplicity in randomised trials. 6.8.1 Subset analysis. 6.8.2 Multi--centre analysis. 6.8.3 Cluster randomization. 6.8.4 Multiple endpoints and treatments. 6.9 Using historical controlsaeo. 6.10 Data--dependent allocation. 6.11 Trial designs other than two parallel groups. 6.12 Other aspects of drug development. 6.13 Further reading. 6.14 Key points. Exercises. 7. Observational Studies. 7.1 Introduction. 7.2 Alternative study designs. 7.3 Explicit modelling of biases. 7.4 Institutional comparisons. 7.5 Key points. Exercises. 8. Evidence Synthesis. 8.1 Introduction. 8.2 'Standard' meta--analysis. 8.2.1 A Bayesian perspective. 8.2.2 Some delicate issues in Bayesian meta--analysis. 8.2.3 The relationship between treatment effect and underlying risk. 8.3 Indirect comparison studies. 8.4 Generalised evidence synthesis. 8.5 Further reading. 8.6 Key points. Exercises. 9. Cost--effectiveness, Policy--Making and Regulation. 9.1 Introduction. 9.2 Contexts. 9.3 'Standard' cost--effectiveness analysis without uncertainty. 9.4 'Two--stage' and integrated approaches to uncertainty in cost--effectiveness modeling. 9.5 Probabilistic analysis of sensitivity to uncertainty about parameters: two--stage approach. 9.6 Cost--effectiveness analyses of a single study: integrated approach. 9.7 Levels of uncertainty in cost--effectiveness models. 9.8 Complex cost--effectiveness models. 9.8.1 Discrete--time, discrete--state Markov models. 9.8.2 Micro--simulation in cost--effectiveness models. 9.8.3 Micro--simulation and probabilistic sensitivity analysis. 9.8.4 Comprehensive decision modeling. 9.9 Simultaneous evidence synthesis and complex cost--effectiveness modeling. 9.9.1 Generalised meta--analysis of evidence. 9.9.2 Comparison of integrated Bayesian and two--stage approach. 9.10 Cost--effectiveness of carrying out research: payback models. 9.10.1 Research planning in the public sector. 9.10.2 Research planning in the pharmaceutical industry. 9.10.3 Value of information. 9.11 Decision theory in cost--effectiveness analysis, regulation and policy. 9.12 Regulation and health policy. 9.12.1 The regulatory context. 9.12.2 Regulation of pharmaceuticals. 9.12.3 Regulation of medical devices. 9.13 Conclusions. 9.14 Key points. Exercises. 10. Conclusions and Implications for Future Research. 10.1 Introduction. 10.2 General advantages and problems of a Bayesian approach. 10.3 Future research and development. Appendix: Websites and Software. A.1 The site for this book. A.2 Bayesian methods in health--care evaluation. A.3 Bayesian software. A.4 General Bayesian sites. References. Index.

Bayesian approaches to clinical trials and health-care evaluation

Background Bayesian methods may be defined as the explicit quantitative use of external evidence in the design, monitoring, analysis, interpretation and reporting of a health technology assessment. In outline, the methods involve formal combination through the use of Bayes's theorem of: 1. a prior distribution or belief about the value of a quantity of interest (for example, a treatment effect) based on evidence not derived from the study under analysis, with 2. a summary of the information concerning the same quantity available from the data collected in the study (known as the likelihood), to yield 3. an updated or posterior distribution of the quantity of interest. These methods thus directly address the question of how new evidence should change what we currently believe. They extend naturally into making predictions, synthesising evidence from multiple sources, and designing studies: in addition, if we are willing to quantify the value of different consequences as a 'loss function', Bayesian methods extend into a full decision-theoretic approach to study design, monitoring and eventual policy decision-making. Nonetheless, Bayesian methods are a controversial topic in that they may involve the explicit use of subjective judgements in what is conventionally supposed to be a rigorous scientific exercise. Objectives This report is intended to provide: 1. a brief review of the essential ideas of Bayesian analysis 2. a full structured review of applications of Bayesian methods to randomised controlled trials, observational studies, and the synthesis of evidence, in a form which should be reasonably straightforward to update 3. a critical commentary on similarities and differences between Bayesian and conventional approaches 4. criteria for assessing the reporting of a Bayesian analysis 5. a comprehensive list of published 'three-star' examples, in which a proper prior distribution has been used for the quantity of primary interest 6. tutorial case studies of a variety of types 7. recommendations on how Bayesian methods and approaches may be assimilated into health technology assessments in a variety of contexts and by a variety of participants in the research process. Methods The BIDS ISI database was searched using the terms 'Bayes' or 'Bayesian'. This yielded almost 4000 papers published in the period 1990-98. All resultant abstracts were reviewed for relevance to health technology assessment; about 250 were so identified, and used as the basis for forward and backward searches. In addition EMBASE and MEDLINE databases were searched, along with websites of prominent authors, and available personal collections of references, finally yielding nearly 500 relevant references. A comprehensive review of all references describing use of 'proper' Bayesian methods in health technology assessment (those which update an informative prior distribution through the use of Bayes's theorem) has been attempted, and around 30 such papers are reported in structured form. There has been very limited use of proper Bayesian methods in practice, and relevant studies appear to be relatively easily identified. Results Bayesian methods in the health technology assessment context 1. Different contexts may demand different statistical approaches. Prior opinions are most valuable when the assessment forms part of a series of similar studies. A decision-theoretic approach may be appropriate where the consequences of a study are reasonably predictable. 2. The prior distribution is important and not unique, and so a range of options should be examined in a sensitivity analysis. Bayesian methods are best seen as a transformation from initial to final opinion, rather than providing a single 'correct' inference. 3. The use of a prior is based on judgement, and hence a degree of subjectivity cannot be avoided. However, subjective priors tend to show predictable biases, and archetypal priors may be useful for identifying a reasonable range of prior opinion.

/pdf/bayesian-methods-in-health-technology-assessment-a-review-4j5dc5afcw.pdf

Bayesian methods in health technology assessment: a review.

Bayesian methods are presented for assessing bioequivalence for studies in which a new formulation and a standard are administered simultaneously, and for Latin square designs which compare two or more new formulations to a standard. Two examples illustrate the application of the methods.

On Bayesian methods for bioequivalence.

Bayesian Approach to Bioequivalence Assessment: An Example

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Bayesian Approach to Bioequivalence Assessment: An Example